Question

Determine whether order is important when translating each verbal phrase into an algebraic expression. Explain.

a) Yes, order is important.
b) No, order is not important.
c) It depends on the phrase.
d) The question is not clear.

Answer 1

The importance of order in translating a verbal phrase to an algebraic expression can vary; it is often crucial but can be irrelevant for certain operations due to the Commutative Property. The correct answer is c) 'It depends on the phrase'.

Step-by-step explanation:

When translating a verbal phrase into an algebraic expression, the importance of order can vary, and the correct response option is c) It depends on the phrase. In mathematics, expressions adhere to the Commutative Property, which states that in addition and multiplication, the order of the numbers does not affect the result, as in a + b = b + a or ab = ba.

However, in subtraction and division, the order is crucial: a - b ≠ b - a and a/b ≠ b/a unless b equals a or both are zero. Similarly, the order of operations (PEMDAS/BODMAS) must be honored to ensure accurate results. When constructing a mathematical model or expression from a real-world situation or verbal description, the order in which things are mentioned might imply sequence, priorities, or other relationships that must be preserved in the algebraic expression to maintain correctness.